In previous studies, transport of solar energetic particles in the inner heliosphere was regarded as one-dimensional along the Archimedean field spiral; i.e., any perpendicular transport is neglected. We extend Roelof’s equation of focused transport for solar energetic particles to accommodate perpendicular transport in the plane of the ecliptic. Numerically, this additional term is solved with an implicit Laasonen scheme. In this first approximation, it is solved for azimuthal instead of perpendicular transport – these are similar in the inner heliosphere where the Archimedean field is almost radial. The intent of the study is to estimate the possible influence of perpendicular transport, but not to fit energetic particle events; thus, the particle source stays fixed on the Sun. For typical ratios κ ⊥ /κ ‖ between 0.02 and 0.1 at 1 AU scaled with r 2 as suggested in nonlinear guiding-center theory, we find that i) an azimuthal spread over some 10° occurs within a few hours, ii) the variation of maximum intensities with longitude is comparable to the ones inferred from multispacecraft observations, and iii) on a given field line, intensity and anisotropy-time profiles are modified such that fits with the two-dimensional transport model give different combinations of injection profiles and mean free paths. Implications for the interpretation of intensity and anisotropy-time profiles observed in interplanetary space and consequences for our understanding of particle propagation and acceleration in space are discussed.